**4. Orbitally shaken bioreactor**

The process engineering and numerical characterisation of orbitally shaken systems poses some challenges for the user. First, the system must be defined. There are different designs of the most common system, the shake flask, be it in shape (Erlenmeyer, Fernbach, Thomson, etc.), sensor installation, diameter of the flask, the neck, or in the material (various plastics and borosilicate glass) [26–29]. In addition to the obvious parameters such as filling height and shaking rate, often neglected aspects such as the shaking amplitude or the contact angle of the material, which depends on the material properties (hydrophilic or hydrophobic), have a decisive influence on the oxygen transfer rate and the power input [30]. This can be explained by the fact that the power is transferred through the vessel wall into the suspension. Likewise, the liquid film that forms on the vessel wall plays a decisive role in the oxygen transfer, as this significantly increases the gas-liquid interface [31]. Finally, in orbitally shaken systems, effects such as the "out of phase" phenomenon can occur, whereas unfavourable cultivation parameters can cause an increase in shaking rate and lead to a decrease in power input, mixing efficiency, and oxygen transfer [32]. Therefore, great care must be taken when choosing simulation parameters and

**Figure 9.**

*Simulation (left) and experiment (right) of the fluid flow in a 500 mL shake flask with 150 mL of working volume at 160 rpm and 25 mm shaking amplitude. The dashed red line indicates the empirically calculated maximum fluid height according to Büchs et al. [33], which deviates by only 2% from the simulated one.*

validating simulated orbitally shaken systems. In the first example, the numerically determined fluid motion and the height of the forming sickle are compared with empirical calculations and experiments (**Figure 9**). The simulations were performed using OpenFOAM v9, the VOF method with the interFOAM solver, and the k-*ω*-SST turbulence model [34]. The CAD model of the 500 mL shake flask was created according to the geometry of Corning Inc.. For glass flasks, ISO 1773 and ISO 4797 could be used [35, 36]. The mesh created by snappyHexMesh consisted of 742,680 mesh cells. The simulation was run transiently for 20 s, using mesh motion (rather than manipulating the force vectors), with a maximum Courant-Friedrichs–Lewy (CFL) number of 0*:*9. For experimental validation purposes, a flask filled with phenol red coloured water was shaken under identical conditions and the liquid movement was recorded. The calculation was based on an empirical estimation according to Büchs et al. [33], who developed a system of 16 equations to be solved iteratively, that allow the maximal fluid height to be derived. The comparison of the maximum sickle heights showed very good agreement. This was 0.0461 m for the numerical approach, 0.0475 m for the experimental verification, and 0.0469 m for the empirical calculation.

Simulations of sickle height and general fluid motion are ideal for performing an initial verification of the accuracy of a simulation. The second example demonstrates the influence of the contact angle on the power input in shake flasks. The experimental determination of the power input in shake flasks has been described for a wide variety of parameter combinations by Büchs et al. [37, 38]. Glass flasks filled with water were primarily used, with contact angles between 13<sup>∘</sup> and 44<sup>∘</sup> being reported in the literature [39, 40]. **Figure 10** compares experimentally measured data from 250 mL shake flasks (25 mL working volume and 25 mm shaker amplitude) to simulations with contact angles ranging from 30<sup>∘</sup> to 75<sup>∘</sup> . Büchs et al. [37] determined

*Computational Fluid Dynamics for Advanced Characterisation of Bioreactors Used… DOI: http://dx.doi.org/10.5772/intechopen.109849*

**Figure 10.**

*The specific power input for 250 mL shake flasks, which were shaken with an amplitude of 25 mm and different shaking rates. Different contact angles were investigated by CFD and compared with the experimental data from Büchs et al. [37].*

specific power inputs from 0*:*1 kW m<sup>3</sup> to 3 kW m3, while the results from the CFD simulations ranged from 0*:*04 kW m<sup>3</sup> (30<sup>∘</sup> , 120 rpm) to 4*:*4 kW m<sup>3</sup> (75<sup>∘</sup> , 360 rpm). Good agreement between simulation and measurement was shown at a contact angle of 30<sup>∘</sup> . With higher contact angles, the power input increased, which must be taken into account when changing from glass to (single-use) plastic flasks.
